Calculus Foundations: Limits, Continuity, and Differentiability for JEE

Mastering calculus is one of the most critical steps to scoring high on competitive engineering entrance exams. Understanding how functions behave at their limits, where they break, and how they change forms the foundation for all advanced mathematical analysis. This comprehensive text-based course offers a clear, step-by-step guide to mastering limits, continuity, and differentiability. Through detailed written explanations, structured mathematical proofs, and solved practice problems, you will build the analytical skills needed to solve complex calculus problems with speed and precision. What you will learn: Understand the fundamental concept of limits, including one-sided limits and indeterminate forms; Apply algebraic simplification, L'Hopital's rule, and expansion methods to evaluate complex limits; Define and analyze continuity of functions at a point and over an interval; Determine differentiability and identify points of non-differentiability using first principles; Solve rigorous calculus problems designed to match the pattern of competitive engineering exams. The course begins with foundational definitions and graphical interpretations of limits before moving into advanced evaluation techniques. You will then progress systematically through continuity theorems and differentiability proofs, reinforcing your learning with written step-by-step exercises. This course is designed for high school students, engineering aspirants, and beginners looking to build a rock-solid foundation in calculus. No prior advanced calculus knowledge is required, though basic algebra and trigonometry are helpful. Start reading today to master the core pillars of calculus and boost your exam preparation.